Natural localized molecular orbital occupied

Still another measure of electron delocalization can be seen in the forms of natural localized molecular orbitals (NLMOs).i By construction, each NLMO remains as close as possible to a parent NBO but includes the weak delocalization tail necessary to preserve exact double occupancy. A determinant of doubly occupied NLMOs is therefore unitarily equivalent to the standard MO determinant, and the Lewis-type NLMOs are able to describe all observable properties of the system just as well as canonical MOs. The perturbative expression (Equation 7.6a) approximates the form of the Lewis-type NLMO a B with parent NBO and weak delo-... 

Photoelectron studies of (CH3)3P=CH2 have provided data on the energy of the highest occupied molecular orbital and some of the lower-lying states (4-9). The frontier orbital energy of 6.81 eV is very low and seems to illustrate the carbanionic nature of the carbon, where this orbital is largely localized. This is borne out by semiquantitative CNDO/2 calculations on this molecule. The orbital sequence obtained is satisfactory according to ab initio results. 

Despite the quantitative victory of molecular orbital (MO) theory, much of our qualitative understanding of electronic structure is still couched in terms of local bonds and lone pairs, that are key conceptual elements of the valence bond (VB) picture. VB theory is essentially the quantum chemical formulation of the Lewis concept of the chemical bond [1,2]. Thus, a chemical bond involves spin-pairing of electrons which occupy valence atomic orbitals or hybrids of adjacent atoms that are bonded in the Lewis structure. In this manner, each term of a VB wave function corresponds to a specific chemical structure, and the isomorphism of the theoretical elements with the chemical elements creates an intimate relationship between the abstract theory and the nature of the... 

The non-linear optical properties of a glass depend not only on the occupied electronic states but also on the unoccupied orbitals, demanding a theory which can treat both sets of states. The unoccupied molecular orbitals are typically diffuse in nature, a "local excitation" involving atomic orbitals of a considerable group of neighboring ions. 

The highest singly occupied molecular orbital is responsible for the radical reactivity of the complexes. Therefore, theoretical computations to elucidate the nature of this orbital are a valuable tool to characterize the localization of the spin density and, even more important, the reactivity of the organometallic radicals. This topic will be further discussed in a later section. 

The employed set of noncanonical orbitals are local in nature the occupied orbital space is represented by localized occupied molecular orbitals, and the virtual (unoccupied) orbital space consists of atomic orbitals (AOs) projected into the virtual orbital space to ensure the required orthogonality of the occupied and unoccupied spaces. 

It is important to note that many metallic properties, such as the Knight shift and the Korringa relationship, are determined by the finite and quasiFermi level local density of states ( p-LDOS). In the approximation most familiar to chemists, what this means is that the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap in metals is much smaller than the thermal energy kf,T, and the value of the / f-LDOS reflects the frontier orbital contributions in a metallic system [23]. The /ip-LDOS also represents a crucial metal sxudace attribute that can serve as an important conceptual bridge between the delocalized band structure (physics) picture and the localized chemical bonding (chemical) picture of metal-adsorbate interactions. 

In contrast to VBT, "full-blown" MOT considers the electrons in molecules to occupy molecular orbitals that are formed by linear combinations (addition and subtraction) of all the atomic orbitals on all the atoms in the structure. In MOT, electrons are not confined to an individual atom plus the bonding region with another atom. Instead, electrons are contained in MOs that are highly delocalized—spread across the entire molecule. MOT does not create discrete and localized bonds between neighboring atoms. An immediate benefit of MOT over VBT is its treatment of conjugated tt systems. We don t need a "patch" like resonance to explain the structure of a carboxylate anion or of benzene it falls naturally out of the delocalized nature of the MOs. The MO models of simple molecules like ethylene or formaldehyde also lead to bonding concepts that are pervasive in organic chemistry. 

Hence, after a decade of false starts, chemists finally learned that the correct basis set should consist of functions that could represent the atomic Hartree-Fock orbitals plus allow for contraction and polarization corrections in the region where they are largest. Similarly it was realized that the Hartree-Fock virtual molecular orbitals were too diffuse for representing the correction to the SCF wavefunction due to electron correlation. Rather, correlation effects are best represented using excitations to nonphysical molecular orbitals that are of the same size as the occupied MOs. Initially this was learned by transforming existing wavefunctions to natural orbital form. Later, MCSCF orbital optimizations were used to obtain these localized correlating orbitals. 

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